Big Idea:
Students will practice rounding both addends to find the estimated sum and both the subtrahend and the minuend to find the estimated difference.

For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation. For this Number Talk, I modeled and encouraged students to solve the problem using mental math and then to show their thinking on their whiteboards. Before beginning, I modeled how to use decomposing: Modeled Addition.

Task 1: 89 + 56

For the first task, students decomposed and solved in a variety of ways, some more organized than others: 89+56 Example A, 89+56 Example B, 89+56 Example C. However, it was wonderful to see that all student white boards looked differently instead of fitting a specific mold.

Prior to starting this Addition and Subtraction Unit, almost all of my students were comfortable and familiar with the standard addition and subtraction unit due to number talks and homework practice.

Reasoning for Teaching Multiple Strategies

During this Addition and Subtraction Unit, I truly wanted to focus on Math Practice 2: Reason abstractly and quantitatively. I knew that if students learned multiple strategies of adding and subtracting numbers, I wouldn’t only be providing them with multiple pathways to learning, but I would also be encouraging students to engage in “quantitative reasoning” by “making sense of quantities and their relationships in problem situations.” By teaching students how to use a variety of strategies, such as using number lines, bar diagrams, decomposing, compensating, transformation, and subtracting from nines, I hoped students would begin to see numbers as units and quantities that can be computed with flexibility.

Goal

I began today's lesson by explaining the goal written on the board: Fourth graders, today's math goal is very important: I can use rounding to check for reasonableness when adding multi-digit numbers. I asked students: Does anyone know what reasonableness means? One student said, "If a price is reasonable, that means that it is fair." I added on: Has anyone ever calculated numbers in math and gotten an answer that just doesn't seem right? When we check for reasonableness, we check to make sure the answer makes sense... and that it's not too high and not too low. We continued by discussing the importance of checking the reasonableness of answers.

Vocabulary

We then moved on to key vocabulary: Today, I really want to make sure you are using high-level math vocabulary when you are turning and talking about the reasonableness of answers. By teaching math vocabulary, students will have the tools to truly practice MP 3 (Constructing Viable Arguments).

I first taught students the terms, addend and sum, using the Addition Vocabulary Poster. After teaching new vocabulary, I always give students time to absorb the new information by turning and talking: Tell someone next to you what the sum is! Next, I used the Algoritm Poster to teach the meaning of algorithm. Finally, I taught students the meaning of checking for reasonableness using the Checking for Reasonableness Poster. You will see that on each of these posters, I tried to provide a definition and an example to aid student understanding.

Modeling the Addition Algorithm & Checking for Reasonableness

In order to model teach my class how to check addition problems for reasonableness, I showed students the following problem: 6,311 + 268 and asked them to solve it on their white boards alongside of me (step by step). I first lined the numbers up in "algorithm form" and discussed the importance of lining digits up. Then, I modeled the process of solving the standard algorithm: First, we add 1 + 8. What's 8 + 1? Next, we add 1 + 6. What's 1 + 6?... I continued modeling in this fashion until we arrived at the sum: 6,579.

Then, I asked: How do I know this answer is reasonable or unreasonable? What can I do to check for reasonableness? Looking back at the goal for the day, students responded, "We need to round!" You're right! What should we round 6,311 to? What should we round 268 to? Could we round to the nearest thousand? How about the nearest hundred or the nearest ten? Should we try all three ways? I then introduced the "approximately equal to sign" (below) and modeled all the Ways to Round on the board. We then discussed which way of rounding was most helpful for checking the answer to the original addition problem. Students quickly caught on to the idea that rounding to the nearest ten gets you closer to the exact answer than rounding to the nearest thousand.

We then moved on to 6,311 + 1,268. Students immediately responded, "That's just a thousand more than the last problem." I love when they look for and make use of structure (Math Practice 7)! Again, we walked through the steps of a standard algorithm. I modeled how to solve on the front board while students solved on their white boards. After arriving at the solution, we again discussed the various ways we could round to check the reasonableness of our solution. Once again, we tried rounding to the nearest ten, hundred, and thousand: Ways to Round 2. Again, students arrived at the same conclusion as before: The further to the left that you round, the farther away from the exact answer. However, the further to the right, the more challenging it is to check for reasonableness. I was hoping that they would notice this!

Resources

To help students meet today's goal, I wanted them to practice solving the algorithm and checking their answers by rounding so I choose the following practice page from the Grade 4 Module 1 Engage New York Unit found online:

At first, I asked students to solve each problem using the standard algorithm. During this time, I conferenced with students and checked for understanding. I loved listening to this student explain how she decomposed numbers in her head to make ten: Using the Standard Algorithm.

When I first started conferencing with this next student, he said, "This is confusing!" It turns out that really what he struggled most with was remembering all the algorithm steps and remembering his addition math facts: Importance of Math Facts.

Once finished, I asked students to check their work with a partner. I do this specifically to support Math Practice 3 (Construct Viable Arguments) and to provide students with opportunities to discuss possible mistakes when they have arrived at two different answers.

Practice Checking for Reasonableness

After students completed the practice page, I modeled how to use Rounding to Check each problem for reasonableness. Students got right to work! During this time, I asked guiding questions, such as: How do you know your answer is reasonable? Here's an example of a student conference during this time: Estimating 34,698 + 7,1840.

Big Idea:
Order of Operations is essential to all math work, leading to understanding of Algebraic expressions. Many Real World Problems take more than one step to solve, sometimes 2 steps and sometimes more steps!